#6017 ⟨
a
,
b
,
c
|
ab
=
c
,
aba
=
ba
⟩
Up:
Monoid enumeration
Prev:
#6013
⟨
a
,
b
,
c
|
ab
=
c
,
aac
=
cc
⟩
Next:
#6019
⟨
a
,
b
,
c
|
ab
=
c
,
aba
=
bc
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
a
is not injective:
b
⋅
a
=
ca
and
c
⋅
a
=
ca
, however
b
≠
c
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Reduction order:
Left-to-right shortlex with
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
c
[1]
2.
ba
⇒
ca
[2]
3.
bc
⇒
c
2
[4]
4.
aca
⇒
ca
[3]
5.
a
c
2
⇒
c
2
[5]
# abc:ab=c,aba=ba acb - - ab=c ba=ca bc=cc aca=ca acc=cc